Last week’s post about the Guyton-Klinger Dynamic Withdrawal Rule only scratched the surface and we ran out of time and space. So, today we like to present some additional and detailed simulation data to present at least four areas where Guyton and Klinger are quite confusing and misleading:

- The ambiguity between withdrawal
*rates*and withdrawal*amounts*. A casual reader might overlook the fact that the withdrawal*amounts*may very well fall outside a guardrail range. Inexplicably, Guyton and Klinger are very stingy with providing information on withdrawal amounts over time. There aren’t any time series charts of actual withdrawals in their paper. - True, Klinger shows time series charts in this paper, but they are only for the
*median*retiree. Does anyone else see a problem with that? The good old 4% rule did splendidly for the median retiree since 1871 so I haven’t really learned anything by looking at the median. Wade Pfau showed (with a Monte-Carlo study) that the GK rule has a 10% chance of cutting withdrawals by 84% after 30 years. It’s very suspicious that the inventors of the rule don’t show more details about the distribution of withdrawals. You could call this either deception or invoke Hanlon’s Razor and blame it on sloppiness and incompetence, and both options are not very flattering. - The Guyton-Klinger rule (even with a 4% initial withdrawal rate) is very susceptible to equity valuations. Results look much worse if you look at the average past retiree with an elevated CAPE ratio (20-30).
- Guyton-Klinger doesn’t afford you to miraculously increase your withdrawal amount without any drawback. The higher the initial withdrawal amount the higher the risk of massive spending cuts in the future.

So, let’s get cranking! We present another case study, the dreaded January 2000 retirement cohort, and also subject the Guyton-Klinger Rule to the whole ERN retirement withdrawal simulation engine to see how all the different retirement cohorts going back to 1871 would have fared. That’s over 1,700 cohorts because we insist on doing our simulations monthly, not annually.

We use real, CPI-adjusted returns for stocks and bonds up to December 2016 and then extrapolate equity and bond returns the same way we described in our initial SWR post and in the 2000-2016 case study. If you don’t like that extrapolation exercise up to December 2019, feel free to ignore those data points.

In the chart below we plot the CPI-adjusted real portfolio values under the static 4% rule and the three different Guyton-Klinger rules. The same parameters as last week. The 4% rule looks pretty grim, having exhausted more than 50% of its initial value and quickly depleting more even if equities continue with 6.6% real returns for the next few years.

Not so the GK rules: The 4% rule is now back to over 80% and could as well grow back to 90% of the initial value. The GK-5% rule is hanging in there pretty well and only the GK-6% rule looks a little bit shaky, in that it’s stuck at only 60% of the initial real value and not able to recover even if returns are average the above average priced S&P500 index.

So far, so good. But just as last week, the time series of actual withdrawal amounts looks not so appetizing. Specifically, all of the GK rules experienced a 50%+ drop in their actual withdrawals and by the end of 2016, they are still between 30 and 40% below their initial withdrawal amount. What’s worse, even with pretty decent extrapolated returns going forward in 2017-2019, withdrawals are stuck at that reduced level.

So, Guyton-Klinger would have been a major letdown for the January 2000 retirement cohort. Especially the initial withdrawal rates above 4% would have caused large and permanent declines in real withdrawal amounts.

Of course, we can go only so far with case studies, so we were curious how all the different retirees between 1871 and 2015 would have fared with the Guyton-Klinger rule. Probably better than the crazy worst case scenarios of 1966 and 2000, but how much better?

Let’s look at how the GK rule with a 4% initial withdrawal rate would have fared for retirees between 1871 and 2015. This is for all retirees regardless of initial CAPE Ratio. Also, we don’t want to show just the median but also some left tail stats, namely the minimum withdrawal, the 10th percentile and the 25th percentile. See chart below:

It turns out the median hardly sees any spending cut. The 25th percentile suffers a 20% cut and manages to recover back to 100% after 19 years. The 10th percentile sees a 40% cut and no recovery back to the initial CPI-adjusted amount within 30 years. Just for the record, I find the GK rule better than the static 4% rule because I’d rather cut my consumption by 40% with a 10% probability than run out of money with a 5% probability. But the tail risk scenarios are not appetizing. And we’re not talking about the 0.00001% tail event, but the 10% lower tail! I would consider myself quite risk averse and if the 10th percentile looks awful this rule would be a non-starter. Even folks who are less risk-averse should probably worry at least about the 25th percentile.

Last week we also pointed out the crucial distinction between real inflation-adjusted withdrawal amounts and the withdrawal rates. Withdrawal amounts can have wide swings, while withdrawal rates stay inside the Guyton-Klinger guardrails for the most part.

*(side note: There is one exception namely when a market move is large enough that even the x=0.10 adjustment will not take the observed withdrawal rate back inside the guardrails and it takes two months of adjustments to accomplish that. So, don’t be surprised to see a very small percentage of months with rates outside the guardrails.)*

In any case, let’s look at the distribution of (real) withdrawal amounts and withdrawal rates over the entire 360 months and all 1,700+ cohorts, see chart below. The top portion is what we really care about, how much we can consume, specifically the percentage of observations that fall into various buckets. The bottom portion is the less-informative figure because that % is multiplied by the current portfolio value, i.e., a moving target. Also, I added three dividers to split the buckets into four sections: Below the lower guardrail (<3.2% in this example), between the lower guardrail and the initial withdrawal rate (3.2-4.0%), between the initial withdrawal amount and the upper guardrail (4.0-4.8%) and above the upper guardrail (4.8%+).

The good news: Guyton-Klinger will likely generate higher withdrawal amounts than the initial. 48.1% of the time we’d even be above 1.2-times above the initial amount. That’s as expected because we already know that the naive 4% rule would have created massive over-accumulation of wealth and the GK rule simply harvests the excess gains.

But GK also forces your withdrawals to below the initial value with a significant probability. 15% probability to withdraw less than 80% of the initial (again, there ‘s no guardrail for the withdrawal *amounts*, only for the *rates*). 20.9% probability of falling into the 0.8 to 1.0-times the initial amount.

As we pointed out in our post on equity valuations, it’s risky to average over all equity valuation regimes when we already know that today we’re in a world of much more expensive equities relative to earnings. So, let’s run the 4%-GK rule only in the months when we had Shiller CAPE ratios of between 20 and 30 (Current CAPE is at 28!).

The chart with the withdrawal amounts doesn’t look so appealing anymore. Sure, the median is hanging in there pretty well; it dips slightly below 4, but recovers by year 16 only to increase substantially after that to more than 50% above the initial withdrawal amount by year 30. Guyton-Klinger did exactly what it was designed to do: scale up the withdrawals when the market cooperates.

But the less fortunate cohorts do much worse. The 25th percentile suffers about two decades of 25% decline of purchasing power. The 10th percentile drops to around 50% below for an entire decade. Of course, both recover back to their original withdrawal amounts but only after 26 and 29 years after retirement, respectively. Ouch!

The same distribution chart as before, see below. You now have a higher than 50% chance of consuming less than the original amount, even a 23.5% percent chance of consuming less than 0.8-times the original amount. All the while, of course, the withdrawal rates stay nicely inside the GK guardrails.

Well, the GK rule was invented to increase the initial withdrawal rate, so let’s see what happens when we push the initial annualized withdrawal to 5% of the portfolio. In the chart below we see that not even the median withdrawal amount can keep up. It drops by a moderate amount, 18% below the initial but it takes almost a quarter century to get back to the initial withdrawal amount. Now even the 25th percentile faces a 50% drop in withdrawals and only recovers after 30 years. The 10th percentile saw a close to 60% drop in consumption and no recovery within 30 years. Not a pretty picture.

The same distribution chart as above, but now looking even grimmer. We spend about one-third of the time withdrawing less than 0.8 times the initial amount, one-third of the time between 0.8 and 1.0 times the initial amount and another one-third above the “promised” 5%. Not a very pretty picture. Does anyone still claim that we can hack our initial withdrawal rate to 5% or more in today’s CAPE regime?

Ok, to be sure, I’m not saying that Messrs. Guyton and Klinger or the folks who are using the rule are dumb. I’m sure they are all very smart individuals. I’m just saying that the GK method leaves me just as clueless about what’s a safe and appropriate withdrawal rate than before I started working on this topic. We saw above that the rule is quite susceptible to the equity valuation regime (just like the dumb static 4% rule).

To see how fundamentally “dumb” the GK rule actually is, let’s try to do the following thought experiment. Imagine we start GK with a withdrawal rate that’s clearly way too low, say 2% p.a. Nobody has ever depleted a portfolio with such a low target withdrawal rate. In fact, even your truly, your crazy cranky Uncle Ern curmudgeon would not argue for a withdrawal rate lower than 2%. Why would anyone cut the withdrawals below the initial amount? It’s completely uncalled for? But that’s what happens in a non-trivial percentage of cohorts, see chart below:

True, you’d eventually withdraw much more. There’s a close to 50% chance of a 60%+ rise in the withdrawal amount, but you’d also have a 20% chance of withdrawals falling below the initial amount. That’s unnecessary!

For full disclosure, we say it again: We like the Guyton-Klinger Rule slightly better than a naive static withdrawal policy like the 4% rule. But Guyton-Klinger suffers from the exact same problems as the 4%: It’s not safe. You replace the small risk of running out of money with the 4% rule with a moderate risk of large spending cuts throughout many years of your retirement with Guyton-Klinger.

As if Guyton-Klinger wasn’t already bad enough with a 4% initial withdrawal rate, jacking up the initial withdrawal rate to 5% or more as GK recommend, especially in today’s environment of expensive equities and low bond yields, would be particularly irresponsible. It’s a bit like sending a novice skier down a double black diamond slope. The helmet (=equivlanet of the guardrails) will likely ensure the poor guy won’t kill himself, but it won’t be a pleasant ride. For us, a dynamic withdrawal rule would have to be a lot smarter than Guyton-Klinger!

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9:
**Dynamic**withdrawal rates (Guyton-Klinger) - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

]]>

Cheers!

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So, here we go, our take on the dynamic withdrawal rates. Jonathan Guyton and William Klinger proposed a dynamic strategy that starts out just like the good old static withdrawal rate strategies, namely, setting one initial withdrawal amount and adjusting it for inflation. However, once the withdrawal rate (expressed as current withdrawal rate divided by the current portfolio value) wanders off too far from the target, the investor makes adjustments. Also, notice that this works both ways: You increase your withdrawals if the portfolio appreciated by a certain amount relative to your withdrawals and you decrease your withdrawals if the portfolio is lagging behind significantly. Think of this as **guardrails** on a road; you let the observed withdrawal rates wander off in either direction, for a while at least, but the guardrails prevent the withdrawal rate from wandering off too far, see chart below. It’s all pretty intuitive stuff, though, as we will see later, the devil is in the details.

The Wall Street Journal calls this methodology “A Better Way to Tap Your Retirement Savings” because it allows *higher *(!) withdrawal rates than the traditional 4% rule. As you probably know by now, we’re no fans of the 4% rule and if people claim that we can push the envelope even further by just applying some “magic dynamic” we are very suspicious. Specifically, we believe that the GK methodology has (at least) one flaw and we like to showcase it here.

See a nice summary here and the original paper here. An interesting link with lots of calculations, examples and an Excel Spreadsheet with sample calculations is here. cFIREsim also simulates the GK method! In any case, the Guyton-Klinger method has four major ingredients, of which three are essential and the fourth seems to be there mostly for “cosmetic” reasons:

- Forego the CPI-adjustment in withdrawals when the nominal portfolio return was negative. Even when doing the CPI-adjustment following a positive return, cap it at 6%, which seems somewhat arbitrary to us.
- (Guard Rail 1) If the withdrawal rate (current withdrawal amount divided by current portfolio value) is greater than 1.2 times the initial withdrawal rate then cut the withdrawal amount by 10%.
- (Guard Rail 2) If the withdrawal rate (current withdrawal amount divided by current portfolio value) is smaller than 0.8 times the initial withdrawal rate then increase the withdrawal amount by 10%.
- Some pretty convoluted mumbo-jumbo on the withdrawal mechanics, e.g., which assets to draw down first, a process they call the
**Portfolio Management Rule**. To us, this seems like a slightly infantile description of a portfolio rebalance back to target weights, i.e., draw down the assets with the highest returns first because they are the ones with the largest overweights relative to the target weights. Why not just do a simple rebalance to target weights then? There are only two possibilities: a) There is**no gain**from their procedure relative to a plain rebalance, then why do it the complicated way? b) There**is an advantage**relative to a simple rebalance but given the ad-hoc nature of their rules, we would argue that any advantage is likely a fluke. In fact, by GK’s own admission (Table 2 in their paper), their portfolio management rule doesn’t add anything when targeting a 90% probability of success and adds only marginally when targeting a 95% probability of success.

- Run simulations at a
**monthly**frequency, rather than annual, to be consistent with our other research on the topic and, of course, for the plain and simple reason that once we are retired we don’t like a whole year worth of withdrawals sitting around in cash every January. We hate leaving money on the table, as you may know from our post on emergency funds. - Since we don’t have all the different equity asset class returns going back to 1871 we simply assume that there is one single equity index (U.S. Large Cap) and one single bond asset (10-year Benchmark U.S. Treasury Bond) as in our previous research, again consistent with our earlier research based on a simple Stock-Bond portfolio
- We discard GK’s convoluted portfolio management rule. We have only two assets (stocks and bonds) and simply assume that the portfolio is rebalanced back to the target weights every month. It’s simpler to model and calculate in our number-crunching software: a simple matrix algebra operation, i.e., we multiply the Tx2 matrix of stock/bond returns with a 2×1 vector of asset weights. Done! No need to carry around time-varying portfolio weights.
- If the 12-month trailing (real) return was negative, then forego the inflation adjustment, i.e., shrink the real withdrawal by the CPI-rate that month. If the 12-month trailing return was positive, then do the CPI-adjustment. We don’t use the Guyton-Klinger 6% cap on the CPI-adjustment, which seems pretty arbitrary and also causes a big loss of purchasing power in the 1970s.
- If the withdrawal rate (current withdrawal amount divided by current portfolio value) is greater than (1+g) times the initial withdrawal rate then cut the withdrawal amount by x. It’s the same setup as in Guyton-Klinger.
- If the withdrawal rate (current withdrawal amount divided by current portfolio value) is smaller than (1-g) times the initial withdrawal rate then increase the withdrawal amount by x. Again, the same as in Guyton-Klinger.

Our take on Guyton-Klinger captures the main ingredients: the guardrails and a decision rule for making vs. skipping the CPI-adjustments, without the baggage of their complicated and likely useless portfolio management rule.

Let’s start with the **good news**. The number one reason we like the GK-rule: If done right it’s (almost) impossible to run out of money with the GK rule (in very stark contrast to the non-trivial probabilities of depleting the portfolio under the naive static withdrawal rule, see our previous research). You heard that right! Our simulations show that if we set the initial withdrawal not too crazy high and we use a tight enough guard rail parameter (g=20%) and aggressive enough adjustment parameter (x=10%) then even under adverse market conditions (e.g., the January 1966 retirement cohort) we won’t run out of money. *(side note: this requires to do the guardrail adjustments throughout retirement, while GK stop doing the adjustments 15 years before the end of the retirement horizon, in which case you do face the risk of running out of money)*

Now for the bad news. We identified one reason to be skeptical, very skeptical, about the Guyton-Klinger rule:

Let’s make this more fun and let me first present the GK simulation results in a very deceptive way to make the dynamic GK rules appear much better than they really are. Let’s see who can spot the deception…

Let’s present a **1966 case study**, the last time in recent history when the 4% rule failed (though you may remember our 2000-2016 case study, where we showed that the 4% rule also looks pretty shaky for the January 2000 retirement cohort). If Guyton-Klinger can succeed here it will succeed almost anywhere! Throughout, we assume an 80%/20% Stock/Bond portfolio and the same return assumptions as outlined in part 1 of this series. We consider 4 different withdrawal strategies:

- The good old 4% rule: set the initial monthly withdrawal rate to 0.333% (=4% p.a.) and then adjust the withdrawals by CPI regardless of the portfolio performance. This method depletes the portfolio after 28 years.
- Guyton-Klinger with +/-20% guardrails and 10% adjustments and a 4% p.a. initial withdrawal rate
- Same as 2, but with a 5% initial withdrawal rate
- Same as 2, but with a 6% (!) initial withdrawal rate

The time series chart of the real, CPI-adjusted portfolio value (normalized to 100 in January 1966) is below:

Holy Mackerel!!! GK beats the 4% rule and it’s not even close. The GK-4% has surpassed the initial $100 (adjusted for CPI!) after 26 years while the old 4% has gone bankrupt after 28 years. The 5% rule is almost back to normal and the 6% rule is hanging in there pretty well, too. Talking about withdrawal percentages, let’s look at those as well, see picture below:

Amazing! Look at the 5% Guyton-Klinger rule. By construction, it stays between 4% and 6% (=5% times 1+0.2 and 1-0.2, respectively), so it never falls below 4% due to the guardrails. Moreover, it has a higher initial withdrawal and a higher final value! It appears to beat the static 4% withdrawal rate in *every* dimension we care about. It looks like the occasional 10% cuts in withdrawals haven’t hurt us too much. Amazing! Have we just found a Safe Withdrawal Rate Nirvana? Let’s nominate Guyton and Klinger for the Nobel Prize! Economics or Peace? Heck, both, of course, and in the same year to save them the travel expenses to Stockholm!

But before you open the champagne bottles, let’s bring us all back to planet earth. **I just scammed you all!** To be sure, the numbers are 100% correct, but the way I presented them was false advertising, even borderline fraudulent.

**Where was the deception I mentioned above?**

Pay close attention to what I **didn’t show** you yet! I never showed you the actual inflation-adjusted withdrawal **amounts**. Who cares about **percentages** of the portfolio value when the portfolio value is a moving target? I want to know the **dollar amounts**. It’s called “Show me the **money**” and not “Show me the **percentages**,” after all. So, how much in CPI-adjusted dollars can I withdraw under the different rules and, specifically, by how much do I have to curb my consumption during retirement due to the withdrawal cuts once we hit the guard rails? That’s displayed in the chart below:

What a disappointment! That’s where the Guyton-Klinger skeletons are hidden. Sure, when your initial withdrawal rate is 5% you never drop below a 4% withdrawal *rate* (due to the guardrail), but it’s 4% of a much-depleted portfolio value, not 4% of the *initial value*. That subtle distinction makes a huge difference. For example, the average withdrawal values for GK under the 4/5/6% initial withdrawal rates are only 2.74%, 3.02%, and 3.22% of the initial portfolio value, respectively. Well, it’s no longer a surprise that we have a higher final value than under the static 4% rule because we withdrew so much less! The advertised 5% withdrawal was only 3.02% withdrawal. What a scam!

Talking about skeletons, here’s more data from the GK horror show: The decline of withdrawals from peak to bottom is a staggering 59%, 66%, and 69%, respectively. Ouch! If you thought that the $1,000,000 portfolio can afford you a $50,000 per year lifestyle using GK, you better plan for a few sub-$20k years and an entire decade (!) of sub-$25k p.a. withdrawals. Suddenly the Guyton-Klinger method doesn’t look so hot anymore.

How is it possible to experience such massive declines in the withdrawals? The GK-rules hide this drop behind the +/-20% guardrails and +/-10% withdrawal adjustments (not to mention the distraction in the form of the asinine “portfolio management rule”) that make it sound like we only suffer relatively minor and temporary decreases in purchasing power. But the 0.2 guardrail is **on top of the drop in the portfolio**. If the portfolio is down by 50% and you hit the lower guardrail, the drop in the withdrawal is (1-0.5)x(1-0.2)=0.4 = 60% under the initial withdrawal. Hence, the large reduction in withdrawals! Skipping the CPI-adjustment in some of the years also erodes the purchasing power.

The claim that we can afford a higher initial withdrawal rate than under the fixed withdrawal rules is a pretty blatant case of false advertising. In fact, this claim has about the same ring to it as the good old “You can afford that big McMansion” or “You can afford that suped-up brand new car.” A 5% initial withdrawal rate may seem nice in the beginning but reality will catch up eventually. The higher you set the initial withdrawal rate the more of a drop in your consumption pattern you might suffer if the market doesn’t cooperate.

We actually have a lot more material and have to defer all of that to a future post. We’re already past 2,000 words and have only scratched the surface. We prepared another case study (the dreaded January 2000 retirement cohort), more comprehensive historical simulations (including the likelihood of a significant long-lasting drop in purchasing power for different CAPE regimes), and like to show several other smaller flaws in the GK methodology. Probably next week!

To wrap up today’s post, the initial question was: Is the Guyton-Klinger method overrated? False advertising sounds more appropriate. The GK-type rules seem to imply that they can offer higher initial withdrawal rates and better long-term success rates. True, but all that comes at the cost of potentially **massive** reductions in withdrawals (50%+ below the initial).

Oh well, what did we all expect? The GK-rules can’t square the circle by offering higher withdrawal rates and lower failure rates. If we wanted to be sarcastic we’d point out that GK won’t cure athletes foot either. If you want to use GK yourself make sure you’re aware of the downside (literally!), i.e., be prepared to curb consumption by 50% if things don’t work out. And that’s not just for a year or two, but potentially for a **decade** or more! That may be doable if your initial withdrawal is $80k or $100k and there is enough downside cushion. But for the folks with a tighter budget, GK would imply a significant probability of heading back to work during early retirement!

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

]]>

We start with an initial real portfolio value, for simplicity scaled to one, make monthly withdrawals, potentially pay or receive some supplemental cash flows (i.e., consulting income during early retirement, social security and pensions later in retirement, health care expenditures later in life, etc.) and then receive a certain stream of capital market returns over time. Given a withdrawal rate, we can easily calculate the final net worth, simply by iterating forward the portfolio value until the final month. But that’s not how we want to compute it. Recall, we target a certain final asset value and desire to calculate the withdrawal rate to exactly match that final value, not the other way around!

One way to calculate the withdrawal rate would be to guess the withdrawal rate, iterate forward, see by how much we miss the target final value and then adjust the withdrawal rate until we hit the desired target. That would work well if we had to calculate one single safe withdrawal rate. But remember: we want to calculate several million safe withdrawal rates (all combinations of starting dates, equity weights, final asset values, retirement horizon, and other parameters), so the trial and error method or even a Newton-Raphson method seem a little bit cumbersome. There is a more elegant method. Much more elegant!

First, let’s define variable *Ct* as the total cumulative return of one dollar invested between the beginning of month *t* and the final period *T*, which is the end of the retirement horizon, e.g., 720 months in our case, or 360 months in the Trinity Study. Think of this as an opportunity cost factors, the loss of each dollar of a withdrawal in period *t* measured in period *T* dollars. If the (real, inflation-adjusted) capital market returns are *r*, then we can calculate this as:

So, the *Ct* are simply the cumulative capital market returns, but moving **backward** rather than forward. Also, note that *C1* is the cumulative return of the initial principal if held over the entire retirement horizon. In other words,

We can now calculate the final asset value of a portfolio with an initial value of one and withdrawals *w* every month as:

The first term on the right side is how much the portfolio would have grown in the absence of any withdrawals, and the second term is the total opportunity cost of all withdrawals translated into date *T* dollars. Notice that even the final month’s withdrawal is subjected to a return *rT* because the withdrawal comes out at the beginning of the month while the final asset value is marked at the end of the final month.

Now we can easily solve for the withdrawal rate w that generates the final value target as

We can also easily expand this analysis to include any sequence of additional cash flows independent of the investment portfolio, *p*, to account for pensions (*p>0*) or even costs in retirement (e.g., kids’ college costs, higher health care costs when old, etc.) that need to be funded over and on top of the baseline withdrawals (*p<0*). Translating those additional flows into date *T* dollars requires multiplying each by its opportunity cost factor and summing up. Hence,

And thus,

Notice how all three terms in the safe withdrawal rate are simply additive. Computationally, this is very easy to handle. For example, for any given retirement start date, horizon, and equity weight, we have to calculate the terms involving *C* only once and simply read off the sustainable withdrawal rates for different values of FV with very little computational burden.

One additional complication we can model is to assume that the withdrawals have a specified scaling/shape over time, i.e.,

and subsequent scaling factors

can take any desired shape, e.g., an exponential increase over time (to model COLA=Cost-of-Living Adjustment above the CPI), or an exponential decay (COLA less than CPI), or any other shape over the retirement horizon. For example, constant for the first 30 years (in real terms) and then declining to account for less consumption demand when older. The SWR calculation is still really simple:

- We are interested in the failure probabilities of different withdrawal rates (say, all values from 3% to 5% in 0.25% steps). cFIREsim would have to calculate a whole new set of simulations with time series of portfolios for each alternative withdrawal rate. We compute one single safe withdrawal rate for each retirement cohort and then simply read off the percentage of our SWR values that were above or below a certain target level.
- cFIREsim has the advantage that it calculates the entire time series of portfolio values. But if you’re only interested in the final portfolio value then it’s very easy to generate that distribution for alternative withdrawal rates without any new simulations. Simply construct the time series of final asset values by plugging in a specific w into one of the “FV=…” formulas above. And again we can do this for different values of w without ever going through the iterative process!

There are obviously others who have already used a similar technique to ours, i.e., computing safe withdrawal rates to hit a specific target:

- For fixed returns, of course, Excel’s “pmt” function calculates a safe withdrawal rate. That’s because, for fixed returns, our formula simply reduces to the good old mortgage amortization math. For example: “=PMT(0.004,720,-1000000,500000,1)” calculates the safe withdrawal rate using 0.4% monthly returns, 720 months, a $1,000,000 initial portfolio (needs a minus operator!!!), with a $500,000 final target. The final argument is set to “1” to indicate that the withdrawals happen at the
**beginning**of the month. Use “0” when the withdrawal happens at the end of the month. - Morningstar has a white paper, thanks to jp6v for pointing that out in the comments section. On page 4 of that document you get a formula similar to ours (though without the final value target FV). And their formula looks more convoluted than it needs to be, but maybe I’m just a math purist.
- A paper posted on SSRN, thanks for jp6v for the reference. Their formula (3) is the same as our base case formula with a final value target. jp6v has a nice summary of that paper on his own blog.
- Another blogger, gummy-stuff with similar formulas to ours and a spreadsheet with his calculations. Thanks again to jp6v for the link.

But we still have the two innovations that I haven’t seen anywhere else:

- The supplemental cash flows, as used in part 4 of the series (Social Security and Pensions).
- The option to do different COLA adjustments, as used in part 5 of the series.

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

]]>

But we still liked the idea of creating a tool to run some quick SWR calculations. In Octave, we can calculate a large number of simulations and calculate safe withdrawal rates over a wide range of parameter value assumptions. Millions and millions of SWRs over many different combinations of parameter values (retirement horizons, final asset value target, equity shares, other withdrawal assumptions). That would have been cumbersome, probably even impossible to implement in Excel. But a quick snapshot on how one single set of SWR parameters would have performed over time? That’s actually quite easy to do, even though there are 1,700+ different retirement cohorts between 1871 and 2015.

- Gold returns are only completely trustworthy after 1968 when I got the London Fixing time series via Quandl. Before that, I had to rely on annual data from OnlyGold.com. If someone has a better (monthly) time series for 1871-1967 please let me know!
- For cash returns I use:
- 3-month T-bill interest rates from the Federal Reserve starting in 1934. Monthly data.
- I have annual data for going back to 1928 from NYU-Stern. Data gathered via Quandl.
- For 1871-1927 I use annual data on 1-year T-bill yields from Prof. Rober Shiller. It’s not exactly ideal to splice it this way but it’s the best I can right now. If someone has better data, please let me know!

**Link to the EarlyRetirementNow SWR Toolbox v1.0**

For obvious reasons, the baseline Google Sheet can only be edited by us. If you like to run your own calculations you have to download your own copy. There are at least two ways to do so:

**(recommended)**Click on Menu, then “Make a Copy” or “Add to MyDrive” to get a local copy of the spreadsheet in your own GoogleDrive. You can then edit the sheet and use your own assumptions.- Click on Menu, then “Download as” then “Microsoft Excel (.xlsx)” to get a copy as an Excel file to store on your own harddrive. It’s not really recommended because most of the formatting will get lost. But if you care only about the computations you should be fine.

- We use monthly data, while cFIREsim uses only annual data.
- We project forward return forecasts beyond 2016 year-end so we can calculate SWR for more starting dates. For example, the January 2000 cohort is already far underwater, as we showed a case study last week. Even aggressive return assumptions will still wipe out the portfolio before too long and we like to count those cohorts as 4% SWR failures even before the utter failure is actually confirmed.
- cFIREsim asks you for a specific withdrawal rate and then simulates how that rate would have performed over time for each of the different starting dates. We go the
**opposite**route: We specify a final value target and our spreadsheet calculates the**exact**initial withdrawal rate that would have precisely matched the final value target. For every retirement cohort between February 1871 and December 2015 (=1,739 months). The advantage of this procedure is that we can then easily calculate the failure rates of different initial SWR without calculating any new simulations. The failure rate of the 4% rate? Simply calculate the share of ERN-SWRs that are greater than 4%. And redo the same for all rates between 3.00% and 5.00% without ever calculating any new set of simulations as would have been required in cFIREsim.

Fields with the orange shading are asking for user inputs:

- The Equity share. We are aggressive and set this to 90%. The residual is invested in 10-year U.S. Treasury Benchmark Bonds.
- The expense ratio: We currently set it to 0.05% p.a. One-twelfth of this is subtracted from each month’s return.
- Equity projected returns post 12/31/2016. These are real annualized return assumptions. In our SWR simulations we set this to 6.6% but here we are a bit more cautious and set this to a more conservative 5.0%.
- Bond returns: for the near-term (notice how low current 10Y yields are) and then longer-term. Short-term we use only 0.5% over the next ten years, then going a bit higher to 2.0% real return after that.
- Same for Cash: We expect pretty low cash returns over the next 10 years (0% real) and then a bit of a bump after that (+1% real).
- Expected future real return for Gold: We set this to +1%. Historically, gold has returned only about 1.5% p.a. after inflation.
- The length of the retirement horizon in months (e.g. 60 years = 720 months)
- The target final asset value as % of the initial portfolio. We set this to 50%.

Below the main parameters, you can also set an entire time series of additional cash flow needs (all monthly numbers as % of the initial portfolio value). For example, we predict to get a pension and Social Security worth about 1% of the initial net worth (in 2018 dollars) 25 years into retirement. So, starting in month 301 we set this value to 1%/12=0.0833%.

That’s all you need. The computer does the rest for you. It calculates the safe withdrawal rates for each month starting in February 1871 to December 2015 that would have exactly matched the final value targeting the last month of the retirement horizon.

Some summary tables are in the first tab “Parameters & Main Results.” Be patient, depending on the internet connection and computer speed it may take a few seconds to recompute all results!

In the table on the left, we calculate the failsafe safe withdrawal rate both over the entire sample and for retirement cohorts post-1950 as well as the 1st, 5th, and 10th percentile. For example, since 1950, a 3.61% withdrawal rate would have failed 5% of the time and succeeded 95% of the time.

On the right, we calculate the failure probabilities of specific rates between 3% and 5% in 0.25% steps, again over the entire sample and since 1950, but also in the three CAPE regimes (<20, 20 to 30 and 30+). In the CAPE 20-30 regime, notice the big jump in the failure rates once you go beyond 3.5%!

We also throw in a chart with the data in the right table:

In the tab “Distribution of Final Value” we can also specify a withdrawal rate and see the distribution of final asset values (real, CPI-adjusted, as multiples of initial). In the example below, we use the 4% rule. We are mostly worried about the left side of the distribution, so final values between the minimum and median. Note how for the median retirement cohort the investor would have grown the portfolio to 8 times (!) its initial real value. The maximum final value would have been a staggering 62-times the initial value. But at the same time, almost 10% of the retirement cohorts ran out of money!

Also make sure you check out the tab “SWR time series,” which includes the SWR for all 1,700+ months in the simulation. For a quick look, there’s a time series chart as well. Notice how there are quite a few times when the SWR is quite substantially below 4%!

Or, in other words, where’s the mega-spreadsheet that has 1,700 rows and 720 columns to iterate over the 60 years worth of portfolio values for the 1,700+ cohorts? We don’t need any of that! The withdrawal rate arithmetic is much easier than that. Stay tuned for next week’s post: our technical appendix with some of the background on the withdrawal rate arithmetic we developed. But if you’re interested, check out how the SWR tab “SWR time series” in Column E are calculated through some pretty trivial calculations from just four auxiliary variables in the tab “Stock/Bond Returns,” columns L through O. Likewise, we calculate the final asset values for the fixed withdrawal rate (column F in that same tab) without ever iterating over 720 months of returns each time we change the withdrawal rate. Much more elegant than the brute-force method in cFIREsim!

As we just mentioned, in calculating the SWR we never even go through the cFIREsim-style exercise of iterating over months and years and plotting the portfolio value time series. That would be too cumbersome for all 1,739 retirement cohorts and several decades of retirement horizon. But if you were wondering how any particular withdrawal rate would have performed over time **for one specific retirement cohort**, here’s the way to do it. Check out the tab “Case Study” where we can add the parameter values, again the orange shaded fields: The retirement start date (year/month), initial portfolio value and the withdrawal rate. And the computer does the rest!

The time series of portfolio values is in column D and also in the time series chart. This will use the same portfolio allocation and also the same supplemental income/expenses as in the main parameter tab. As we already noted last week, January 2000 would have been a pretty bad starting date for retirees. Not just early retirees!

Please read the disclaimers here on the website and in the Google Sheet. We gladly grant the right for others to utilize our work but please make sure to credit us and quote us properly. We do own the copyright to everything we post here!

Also, note what this toolkit is and what it isn’t: It is a toolkit to determine how different withdrawal strategies would have performed **in the past**. It’s not a forecast. Past results are no guarantee of future results! But we can still learn from the past.

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

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- Wade Pfau has been warning that due to high equity valuation and low bond yields the Trinity Study success rates are likely overrated. His argument is similar to ours in Part 3 of this series: we live in a low return world now and comparisons with past average returns could overstate the success probability of the 4% rule. He uses a slightly different methodology (Monte Carlo simulations) but reaches similar results.
- Even Michael Kitces, arguably one of the great defenders of the 4% rule, has (inadvertently?) demonstrated that the 4% rule over 30 years isn’t all that sound. In the discussion after the famous “ratcheting post,” some readers (including yours truly) pointed out that we can’t replicate the success of the 4% rule with 1965/66 starting dates. Nothing to worry about, Kitces replied, all you needed to do is to use a very
*short-term*bond (1-year T-bills) for the bond allocation, and you sail smoothly during the 1970s. Who would put 40% of the portfolio into 1-year Treasury bills (essentially CD interest rate) rather than trying to harvest the term premium of longer-term bonds? Very easy: someone with 20/20 perfect hindsight who knew that longer duration 10Y bonds will get hammered in the 70s and sink the 4% rule even over a 30-year horizon.

And I just became a little bit more skeptical about the 4% rule even over a 30-year horizon! But there is (at least) one prominent 4% SWR firewall still standing. In countless blog posts, discussions, forums etc. I have heard this quote (or variations of it):

“The 4% rule worked just fine during the Tech Bubble and Global Financial Crisis”

Let’s shine some light on that claim.

The first suspicions about the validity of that claim came when I looked at the average returns in equities and bonds since December 31, 1999, and they didn’t look so appealing. Equities (S&P500, dividends reinvested) returned only slightly more than 4% p.a. in *nominal* (!) terms, and 2.36% p.a. in real, CPI-adjusted terms. How can that justify a 4% withdrawal rate? Isn’t the real portfolio return supposed to be roughly equal to the real rate of return to make this work? Below we plot the cumulative returns (before even withdrawing anything!) of different Equity/Bond portfolio mixes, adjusted for inflation.

Note, these are already the returns taking out 0.05% p.a. in ETF expense ratios, hence, the 100% equity portfolio return dropped from 2.36% to 2.31%. None of these portfolios would have stayed even close to a 4% real return target over time. Every month and every year we stay below that black line we dig deeper into the principal. When someone wants to tell me that the 4% did well since 2000, that doesn’t even pass the smell test.

So, without simulating anything I already know that the 4% rule would not have fared very well and you would have wiped out some portion of your principal. How much? Well, let’s run the ERN simulations and see for ourselves. Since we started this series I updated the realized returns all the way to December 2016 (Parts 1 through part 5 used realized returns only up to 9/30/2016). Let’s see how the 4% rule would have performed under different portfolio allocation assumptions. We also took the liberty to extend the equity and bond returns beyond the first 17 years. As described in our initial SWR post, we assume that future real equity returns are equal to the average real return since 1871 (about 6.6% p.a.). We now assume that the bond return is going to be equal to the 12/31/2016 10Y nominal bond yield (around 2.5%) minus 2% inflation = 0.5% p.a. real for the next 10 years, then also returning to its long-term average of 2.6% real.

**Side note:** That’s actually a pretty aggressive estimate for future returns given that the CAPE is so high! Recall our post from last year, where we plotted the current CAPE earnings yield (=1/CAPE) vs 10-year forward equity returns: If the CAPE is above 25 (yield <4%) the 10Y forward equity return never exceeded the 6.6% mean real return, see chart below!

Below is a time series chart of the real portfolio value over time for different equity portfolio shares between 50% and 100%. A portfolio would have taken a serious hit after 17 years: In real terms, the portfolio is down by anywhere between 30% and 75%.

But can the portfolio recover? Well, of course, it can if stocks go up by between 50% and 300% in the next year. But even the somewhat optimistic assumption of 6.6% real equity returns over the next 13 years will only further deplete the portfolio, see the downward-sloping portfolio values starting in 2017.

Next, we can also calculate the SWRs that would have exactly matched a specific final value target after 30 years. Again, that’s using the 17 years of actual return data plus the 13 years of return forecast. See chart below:

In January 2000, you could have withdrawn 4% or more if you weren’t too aggressive on the equity allocation and you’re OK with running out of money after exactly 30 years. 4% probably wasn’t such a bad assumption for regular retirees who were 65 years old in 2000. But early retirees? You probably want to ensure that you have about 75-100% of the initial principal available half-way through your retirement. Depending on the equity weight, 2.6-3.1% for capital preservation and 2.9-3.5% for 75% capital preservation was all you could start withdrawing in 2000. And that’s under the somewhat rosy assumption of 6.6% real equity returns for the next 13 years (despite elevated CAPE ratios) and zero volatility along the way. Not a pretty picture! If anything, the 2000-2016 episode was a worst-case scenario for early retirees. Quite the opposite of the “4% rule did OK” myth.

So, how can one still claim that the 4% rule is A-OK after 2000? We’d have to be deceived by a financial Potemkin Village. I gathered some examples below:

Just to be clear, I am not saying that Kitces wants to deceive anybody in his post on the 4% rule post-2000. He’s obviously an extremely smart guy and puts out very fascinating material. I also found that he’s very kind and gracious in replying to questions and requests.

But his post on the matter is still a Potemkin Village. All the pertinent information is in that post. It’s all 100% accurate, completely confirmed by yours truly. Everybody who **wants** to get an objective picture of the 4% rule in the 2000-2015 period will walk away with the exact same information that I saw:

- The 4% rule worked probably all right for the
**average 65-year-old**who retired in 2000. That person may make it through to 2030, especially considering that the person is now 82 years old and may curb consumption a little bit, in line with losing almost 40% of the real portfolio value. Not so much, though, if there are medical bills piling up and withdrawals actually grow faster than CPI! - But the
**average early retiree**would have trouble making the 4% rule work. By 12/31/2016, only 17 years into the retirement you would have wiped out a big chunk of the portfolio as we show in our calculations above and even then you have to cross your fingers and hope for above average equity returns, something unprecedented when the CAPE is at 28. Good luck with that!

But how about folks who **don’t want** to see the faults in the 4% rule? Say, someone who has a predetermined conclusion that the 4% rule worked great in 2000 even for early retirees. If that person reads the Kitces article he/she will come to the exact opposite conclusion. See the following chart, here reprinted with permission:

Kitces used a 60/40 Stock/Bond mix and now it looks like the year 2000 cohort is back to maybe $930,000. Doesn’t look so bad, right? That proves the 4% succeeded during that time! Not so fast: read the fine print! This is the *nominal* value. $930,000 in *nominal* terms means that the real value is down to somewhere in the low $600,000s, consistent with our calculations.

Also, right after the Kitces post (July 2015) the portfolio value is trending down, see our time series chart above. Recall, that our calculations take into account the pretty impressive 2016 equity return (12% with dividends!) and we’re still continuously melting away our principal! That’s because the 4% withdrawal rate has now grown to a 5.7% to 16% withdrawal rate (depending on the equity share). Remember, there’s only between 25 and 70% of the portfolio left, so the withdrawals are now higher relative to the principal (4%/0.7=5.7%, 4%/0.25=16%). You will eat into the principal even more during the remaining 13 years (and we are not even taking into account equity volatility and Sequence of Return Risk). It may all still work out for the *traditional* retiree with 13 years to go, but not for the early retiree with 40+ years to go.

Recall the “ratcheting post” from Kitces, written in June 2015? Compare that to the post about the 4% during the post-2000 period, written only a few weeks after that, and you will notice one subtle difference:

- In the ratcheting post, the 4% rule worked during the 1970s because the 40% bond allocation was invested in
*short-term*bonds (1-year T-bills). - In the post on the dot-com bubble and global financial crisis, Kitces uses a 10-year Treasury bond.

If you had followed the advice from the ratcheting post and invested in 40% short-term bonds starting in 2000 you would have lost the beautiful diversification benefit of bonds and you would have missed out on the big bond rally. The nominal portfolio value would have gone down to just under $500,000 in nominal dollars and below $350,000 in real, CPI-adjusted dollars by December 31, 2016. Good luck making that money last until even 2025. If you haven’t cut your consumption yet, the annualized rate of withdrawal would be almost 12% now. To bring back the withdrawal rate to a more manageable 4% we’d have to cut withdrawals by about two thirds!

I wonder if all those who tout the 4% rule as so safe realize that in the most optimistic interpretation it will involve timing the bond vs. cash allocation. **Better get your term premium model up and running, everybody! **And the worst possible interpretation is that the success of the 4% rule is based on some pretty blatant data snooping and hindsight bias, even for the traditional retiree with a 30-year horizon.

Strictly speaking, the Trinity Study indeed covers the DotCom bust and the Global Financial Crisis. And it shows that the 4% rule is safe. But only towards the *end* of their 30-year windows. To my knowledge, the most recent installment of the study is from April 2011 with data covering 1926-2009. Therefore, we don’t have any data about the year 2000 retirement cohort yet. Strictly speaking, it will take until December 31, 2029, to get word from the Trinity Study about whether the 4% rule worked with the January 2000 starting date. What if that cohort already runs out of money in 2025? We show that is a real possibility unless stocks return more than their historical average going forward. Will the Trinity Study still be quoted as the defender of the 4% rule for the early 2000s until they actually confirm it didn’t work?

The often quoted statement above needs a few important qualifiers for us to agree with it:

The 4% rule worked just fine during the Tech Bubble and Global Financial Crisis **IF:**

- You have a 30-year retirement horizon.
- You are comfortable depleting your money at the end of that horizon and/or significantly cutting your real withdrawal amounts.
- You had a relatively low equity portion (60% or less).
- You are not a passive investor but rather have the foresight to time long-term vs. short-term bonds. Specifically, you needed the ability (or dumb luck?) to implement the exact allocation that
**didn’t work**in 1965/66 and**avoid**the allocation that**did****actually work**quite beautifully in 1965/66. - Did we miss any other qualifiers? Please let us know in the comments section!

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

]]>

But how about tinkering with the inflation adjustments, also called Cost-of-Living adjustments (COLA)? I often hear that one way to save the 4% rule in periods when the stock market doesn’t cooperate is to not do inflation adjustments for a few years. Or simply utilize the fact that we all potentially spend less (in real terms) as we age! How much can we push the initial withdrawal rate in that case?

The first table in the often cited Trinity Study, apparently the gold standard of retirement research, looks at the success rates of withdrawal strategies that **don’t** do the cost-of-living adjustments (i.e., keep **nominal** withdrawals constant):

Source: Trinity Study (https://www.onefpa.org/journal/Pages/Portfolio%20Success%20Rates%20Where%20to%20Draw%20the%20Line.aspx)

That seems like an interesting exercise to do before jumping into the inflation-adjusted study, right? Wrong! To me, this is a pretty cringeworthy and nonsensical exercise for the following reason. See the chart below where we plot the purchasing power of an initial withdrawal of $40,000 p.a. over 10, 20, 30, and 60 years when foregoing CPI-adjustments:

Not doing inflation adjustments during the 1970s would have implied a massive erosion of purchasing power: Your initial $40,000 withdrawal in 1970 dollars would have been worth only around $8,000 in the year 2000. Not quite a Zimbabwe-style runaway inflation, but still pretty bad. Good luck living your golden years on that amount! On the other hand, in the 1930s you would have massively *increased* your CPI-adjusted consumption in a deeply deflationary decade. So, that retiree would have fared much better (in real consumption terms, not in final value). Lumping them all together and calculating success rates is not very meaningful then. It’s comparing apples and oranges! Sorry to say this, but in my eyes, anybody who looks at safe withdrawal rates in purely nominal terms suffers some serious loss of credibility. It proves that even the combined brainpower of 3 PhDs can create some junk science.

If we want to make the case that people consume less as they age, we should still do the calculations in real space but then shrink the expenses at a certain (real) rate per year, as we propose here. Essentially, chip away a small percentage of the purchasing power every year to account for the fact that we could potentially consume less over time. How much should we shrink consumption (and thus withdrawals) over time? Let’s look at what happens when we do the COLA adjustments as CPI minus *x*% for several different values of *x*, see table below.

After 60 years even a tiny value of *x* will erode our purchasing power by a lot. Personally, we might still be comfortable with 0.5% (around 26% erosion of purchasing power) but certainly not 1.0%. For retirees with a very high initial withdrawal amount, say, $100,000 p.a. it might be possible to go all the way up to *x*=1%, because that would cut down the real withdrawals to a still-generous $54,720. But does anybody want to start at $40,000 at age 30 and shrink the withdrawals to slightly less than $22,000 at age 90? That will be eaten up by medical bills alone. And forget about going to 1.5% or more. So we will study only the 0.5% and 1.0% versions, in addition to the baseline:

**Baseline:**Increase withdrawals in line with CPI**COLA=CPI-1.0%:**Shrink the real withdrawals by 1.0% p.a.**COLA=CPI-0.5%:**Shrink the real withdrawals by 0.5% p.a.

We also throw in another two scenarios of tinkering with the withdrawal amounts over time:

**5Y-no-COLA:**shrink the real withdrawals by 2% for five years and hold them constant after that. Starting in year 6 this would mean that the withdrawals are about 9.6% lower than initially (0.98^5=0.904). That’s the solution often quoted as the panacea to bad market returns early on: simply forego the inflation adjustments for a while. Assuming 2% inflation forecasts over the foreseeable future, this withdrawal pattern would exactly accomplish that. Also, notice we never scale the withdrawal up again. Then a 4% initial withdrawal would mean you consume only about 3.6% of the initial net worth in the long-term.**5Y transition 75%-100%:**Somewhat the opposite of assumption above; gradually smooth into retirement, for example, by preserving some small income source initially and phasing it out over 5 years, or by simply being extremely frugal initially. Withdraw only 0.75 times the long-term target in year 1, 80% in year 2, …, 95% in year 5 and then the long-term target in year 6 and onward. Also notice that if this procedure yields a, say, 3.5% SWR in the simulations, the initial withdrawal rate would only be 2.625% of the initial net worth and we’d scale that ratio up to 3.5% over the next five years.

See chart below for the scaling of withdrawals in real dollars, compared to $100 in the baseline:

As we did last week with the different Social Security assumptions, let’s look at the median increase in the withdrawal rate that the withdrawal pattern affords us, see table below. We calculate this again for all months, for months with the CAPE between 20 and 30 and for months with the CAPE in that range and the baseline SWR<4%. Quite intriguingly, for the first two assumptions you roughly increase the initial withdrawal rate by exactly the 1.0% or 0.5% rate adjustment to the COLA (+0.932% and +0.462%, respectively) when we take the median of all months. But that advantage quickly melts down to only about three-quarters of that amount when taking the median over only the current CAPE regime (20 to 30) and about half when the CAPE is elevated and the baseline 4% rule would have failed (0.558% and 0.275%, respectively). So, the unpleasant fact is that the **COLA-x% works best when we need it the least**. That makes perfect sense: because we have such a front-loaded consumption pattern we get hit by the dreaded **Sequence of Return Risk**!

We get qualitatively similar results with the other two withdrawal patterns. The 5Y-no-COLA adds about a half percentage point (0.519%) to the withdrawals (before taking it away again over the next 5 years!!!) and the 5Y smooth transition into retirement boasts a respectable quarter point increase in the median increase of the SWR (0.244%). But the bump in allowable SWRs melts away again when we take into account today’s high CAPE value and even more when we look at the retirement dates with low enough initial returns that pushed the baseline SWR below 4%. Not a pretty picture.

Next comes a similar table to last week’s; let’s look at the failure probabilities over different initial withdrawal rates, see below. The top part of the table is for today’s CAPE regime. None of the alternative withdrawal patterns offer a failure probability good enough to justify the 4% rule. OK, maybe the CPI-1.0%, where we would push the failure rate to slightly below 10%, but as we said before that would be a bit too aggressive of a cut in consumption for our taste. All other withdrawal patterns still have failure probabilities around 20%, which is completely unacceptable for us.

What the table seems to indicate is that you might gain a 0.25% increase in the SWR for the less aggressive withdrawal rules and 0.50% for the CPI-1.0% rule. In other words, the 3.25% SWR has a 3.1% failure rate in the baseline scenario and with COLA-1.0% we can push all the way to 3.75% SWR to still keep the failure probability in the low single digits. For the other withdrawal patterns, we’re talking 3.50% again, so that’s roughly a quarter point improvement

Why did we use a 100% equity share in the simulations above? It goes back to the earlier findings in the previous parts of the SWR series (especially part 2 and part 3): The success probabilities mostly go up with the equity weight, at least over a 60-year horizon. The only time that’s not true is when right at the start of retirement stocks are seriously overvalued (CAPE>30). But for completeness, we again display the success probabilities over different equity weights, see chart below for a 4% withdrawal rate. The top chart is for all CAPE ratios and the bottom for the CAPE between 20 and 30 (current CAPE is around 28). We confirm again that the success probabilities are almost monotonically increasing in the equity weight:

And the same chart for a 3.5% withdrawal rate. There is again a plateau of 100% (or close to 100%) success rate for high enough equity shares, and that’s true even for slightly overvalued equities (CAPE between 20 and 30). It looks like the sweet spot for less than 100% that exists over 30 years doesn’t carry over to 60 years. It’s the same curse of low bond returns we’ve talked about in the past.

We did this study about tinkering with the COLA anticipating that probably a lot of folks will ask for it. Personally, we don’t plan to mess around with our COLA and the lifecycle spending amounts very much. The little bit of gain in the initial withdrawal rate is not worth the potential for spending cuts later in life when we are least able to earn a supplemental income.

But isn’t it true that people spend less as they age? Yes, that’s what economists have shown but I would ask back: Do people spend less because they **want** to or because the **have** to? Our blogging friend Fritz at Retirement Manifesto had a great post the other day about how woefully unprepared Americans are when it comes to retirement savings. There is some evidence that people spend less in retirement because they have to: Social Security benefits are pretty modest and even adding other supplemental income from retirement savings and annuities, pensions, etc. leaves most retirees still far below the earnings potential of the median household in the 50-65-year age range.

If I were to adjust the lifecycle spending pattern at all, I’d probably *raise* my old-age consumption. We might travel less, but likely prefer to travel in more comfort and at a higher cost. There will be less backpacking and more cruise vacations after I reach age 60! Moreover, we will certainly have higher health expenditures than today. And on healthcare, it’s a double whammy: higher expenses when we get old and likely less help from the government than even today’s retirees are used to. So, in our personal spreadsheet of spending plans, I currently have a scenario where I bump up withdrawals to more than CPI rates after age 70 exactly for that reason. Another reason not to rely on the 4% rule.

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

]]>

**My Top 7 Disagreements With Personal Finance Experts**

Of course, to read it all, you’ll have to head over to Budgets are Sexy. But please see below for supplemental material, i.e., some of our blog posts on the seven topics:

- Safe Withdrawal Rate:
- The Ultimate Guide to Safe Withdrawal Rates – Part 1: Introduction (plus follow-up posts, part 2, part 3, going to part 4 already!)

- Robo-Advisers:
- Emergency Funds:
- Bonds to diversify equity risk:
- Bond vs. Stock Risk:
- Cash as bear market insurance:
- Tax loss harvesting:

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- the sustainable withdrawal rates over 30 vs. 60-year windows (part 1),
- capital depletion vs. preservation (part 2)
- and the current expensive equity valuations (part 3).

The bad news was that after all that number-crunching, the sensible safe withdrawal rate with an acceptable success rate melted down all the way to 3.25%. So much for the 4% safe withdrawal rate! That 25x annual spending target for retirement savings just went up to 1/0.0325=30.77 times. Ouch! Sorry for being a Grinch right around Christmas time!

But not all is lost! Social Security to the rescue! We could afford lower withdrawals later in retirement and, in turn, scale up the initial withdrawals a bit, see chart below. How much? We have to get the simulation engine out again!

Under the current Social Security setup, Mr. ERN is eligible for Social Security at age 62, which is 18 years after the planned retirement. But we will likely wait until Mr. ERN is in his late 60s to maximize the Social Security benefit. That’s roughly 25 years into our 60-year retirement. Together with the benefit from Mrs. ERN and a small legacy pension for Mr. ERN, we expect a total combined annual benefit of about 0.01 times our financial net worth at the start of our retirement. That’s all under the (rosy?) assumption that there are no benefit cuts in Social Security, whether through adjustments in the benefits formula, changes in the retirement age or some form of means-testing. The likelihood of benefit cuts is a whole separate topic for a future post, though.

So, 35 years worth of 1% extra income during a 60-year retirement horizon affords us a 1% / 60 x 35 = 0.583% extra withdrawal, right? Withdraw 3.25%+0.583%=3.833% for the first 25 years and 2.833% for the next 35 years, which combined with the social security benefit generates a fixed real consumption path of 3.833% of initial net-worth. Almost back to 4%, how cool is that? Almost too good to be true! Well, unfortunately, this back-of-the-envelope calculation **is** too good to be true. The time value of money messes up the entire calculation! In other words, Social Security benefits many years in the future are going to be worth a lot less in today’s dollars. And even worse, the dreaded Sequence of Return Risk (SoRR) comes into play here again because we front-load the withdrawals. How much of a haircut do we have to apply to our calculation? We need to look at our simulations to find out.

The baseline simulation (more scenarios below), is what we call “25Y-1%” where we start with a withdrawal rate x% in the first year, inflation-adjust over time and take the withdrawals from the portfolio down by 1 percentage point (also adjusted for inflation) once we draw Social Security benefits. For each possible starting date, we solve for the withdrawal rate that *exactly matches* our final value target (50% of beginning value, in real terms) after 60 years.

In the scatterplot below we do the usual analysis as before: Compare SWRs in two different scenarios: No Social Security (x-axis) vs. our likely Social Security benefits (y-axis). Of course, all dots are above the 45-degree line indicating a higher SWR, but not by much.

Because the scatterplot above was so hard to decipher, let’s plot the **increase** in the SWR due to the Social Security benefits on the y-axis, see chart below. I do this for all months, but I also mark the dots when the CAPE ratio was between 20 and 30 (12/31/2016 CAPE is around 28, according to Professor Shiller, page accessed on January 2, 2017). The increase in the SWR from our Social Security assumption is a lot leaner than the back-of-the-envelope calculation. Bummer! The SWR increase ranges from about 0.12% to just under 0.25%, with a median of around 0.18%. This will not bring our SWR back to 4%!

Same chart as above, but as a time-series chart. Increase in SWR due to Social Security Benefits after 25 years.

We look at a total six scenarios, three starting dates: 20, 25, and 30 years into retirement and two different benefit levels: 1% and 2% of the initial retirement nest egg. So, for example, if you have a $1,000,000 portfolio and expect $20,000 in benefits after 30 years you’d look at the 30Y-2% model. As we mentioned above, our own personal situation comes closest to the 25Y-1% model.

Instead of plotting the scatterplots above, let’s just display one summary statistics table about how much the different Social Security / Pension models increase the SWR, see table below, specifically the median increase. Note that the order is from the smallest to the largest discounted sum of benefits (30Y-25Y-20Y). We calculate the median increase for all months, for months with a CAPE between 20 and 30, and also for months when the CAPE was between 20 and 30 and the baseline SWR was below 4%. We calculated the latter because we wanted to see how much of a difference our Social Security would have made when we really have to rely on it due to bad financial market performance.

In our personal situation, we’d expect a 0.191% increase not conditioning on the CAPE regime, 0.179% for today’s CAPE regime, and 0.164% conditional on actually having to rely on Social Security. Hmmm, slightly disappointing. What’s particularly unfortunate in our calculations is that the increase in the SWR is lower when we need it the most, namely when the CAPE is high and the baseline SWR is already below 4%. Unless you expect very generous benefits, Social Security will not serve as a panacea for the 4% rule!

**A little side note:** Do you notice something in that table above? The incremental effect on the SWR exactly doubles when going from 1% to 2% worth of Social Security benefits. That’s no coincidence. It’s a mathematical result. So if you happen to expect Social Security and/or Pension benefits amounting to, say, 1.3% of your initial net worth, simply take the 1% figure above and multiply by 1.3. I don’t want to bore everybody with the arithmetics behind our calculations, but maybe in a future post, we will do a mathematical appendix, gasp!!! Stay tuned!

We can also look at the failure rates of different withdrawal rates between 3 and 4% in 25bps steps, see table below.

Bottom line: If you’re unlucky and face adverse capital marker returns early on in retirement and you keep withdrawing your initial rate then your portfolio will be so compromised by the time you reach your Social Security age that it won’t make much of a difference anymore.

So, in today’s environment, the highest withdrawal rate we’d personally be comfortable with is 3.5%. That has a 3.9% failure rate. The 4% SWR would have had a 28.8% failure rate in the absence of Social Security and only a pretty generous benefit worth 2% p.a. and 20 years after the retirement would significantly reduce the failure rate to 11.7%. Under all other parameterizations, the failure rates were still around 20%. Unacceptably high!

**Conclusion: Even before accounting for potential future benefit cuts, Social Security benefits will not make a huge difference in the Safe Withdrawal Rate and will most definitely not save the 4% rule!**

Let’s look at some more data tables that cover more assumptions. Hopefully, this can serve as a reference for readers who want to look beyond the ERN family assumptions and see how the failure rates would have looked like in their personal situation.

- Retirement horizon: 60 years (first table) and 50 years (second table). We don’t even display anything below 50 years considering that most folks in the FIRE crowd will retire in their 30s, maybe early 40s.
- Today’s CAPE regime (20-30) in the top half of each table vs. unconditional on CAPE regime in the bottom half of each table, just for reference.
- Three different social security parameters: None at all, 1% benefits after 25 years (ERN family assumption), 2% benefits after 30 years (for example $1,000,000 portfolio and $20k in benefits after 30 years).
- Four different equity shares: 70/80/90/100%. I don’t even go below 70% because the failure rates get so much worse. Also, recall that the bond index I use here is a 10y Treasury index with no credit risk. A 30% allocation to a safe government bond index plus 70% equities roughly corresponds to a 40% allocation to investment grade bonds plus 60% equities. We definitely do not recommend going below that equity allocation to preserve long-term sustainability of the portfolio.
- Capital Depletion vs. 50% final asset target (left vs. right half of table)
- Five different withdrawal rates between 3 and 4% in 0.25% steps.

- Part 1: Introduction
- Part 2: Some more research on
**capital preservation vs. capital depletion** - Part 3: Safe withdrawal rates in different
**equity valuation**regimes - Part 4: The impact of
**Social Security benefits** - Part 5: Changing the
**Cost-of-Living Adjustment**(COLA) assumptions - Part 6: A case study: 2000-2016
- Part 7: A
**DIY withdrawal rate toolbox**(via Google Sheets) - Part 8: A
**Technical appendix** - Part 9: A
**Dynamic**withdrawal rule: Guyton-Klinger - Part 10: Debunking Guyton-Klinger some more
- Part 11: Seven criteria to grade withdrawal rules
- Part 12:
**Dynamic**withdrawal rates based on the**Shiller CAPE**ratio - Part 13:
**Audience suggestions!**

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**Can there be**** **__too little__** ****of a**** **__bad thing__**?**

The bad thing I’m talking about is ** debt**. To many of us in the FIRE community, debt is a four-letter word – figuratively! An entire niche of the Personal Finance blogging world is dedicated to getting out of debt and that’s a really good cause especially for those with a low or negative net worth. Paying off credit card debt at 18-20% or student loan debt with high single-digit percent interest rates should be priority number one. But that doesn’t mean that all debt is bad. For us in the ERN household, we’re blessed to never have had any sizable debt, except for a 30-year mortgage that we plan to pay off not a day earlier than we have to. We enjoy the ultra-low interest rate (3.25%), the tax-deductibility and putting our money to work with higher expected returns elsewhere.

So, in general, we agree that too much debt is bad, but not all bad things are created equal:

It’s my understanding (as a non-medical professional) that cigarettes are bad for you, regardless of the quantity. So are a lot of illicit drugs. We completely agree that some bad things should be avoided at all costs and all the time. But we doubt that debt is one of them!

Alcohol is a dangerous nerve poison that will impact your cognitive abilities in tiny doses, impact your driving at a blood alcohol concentration (BAC) of only about 0.05% and likely kill you at a BAC of around 0.5%. Continuous overconsumption could cause heart disease, fry your liver and mess with your brain to name just a few negative side-effects.

But alcohol consumed in moderation actually has some health benefits. Red wine contains substances with unappetizing names (antioxidants, polyphenols, resveratrol) but they are actually really good for you, see here for the 8 reasons to love red wine. But researchers found that even the *alcohol itself* (!) seems to support your health (see here). Heck, our blogging friend Physician on FIRE recently gave away beer for charity, so ethanol can’t be that bad. The man is an anesthesiologist after all!

What means moderation? About one to two drinks a day seems to be the generally accepted quantity that’s not just safe but even supportive of health and longevity (see Mayo Clinic link), not to mention our quality of life. They didn’t mention that we can safely double the alcohol intake if we live in France, Italy, Spain or Portugal and consume red wine with every meal. But I’m sure I read that somewhere, too.

All right, what is debt then? More like a cigarette to be avoided at all cost or more like alcohol with benefits if applied in moderation? Dave Ramsey and Suze Orman seem to think that debt is like a pack of Marlboro Reds or, even worse, those awful Gitanes with the yellowish paper and no filter. Unhealthy in any quantity, probably unhealthy to even look at!

But have we gone too far in the quest to eradicate debt? Here is some food for thought, seven reasons why we believe that debt and leverage in moderation can be good for us, just like the occasional beer or red wine:

Granted, the most colossal **failures** in business were bankrupted by too much leverage (LTCM, Lehman Brothers, etc.). But that doesn’t mean that successful investors should all use zero debt. Look at real estate investors: whether it’s REITs, or private equity real estate deals, nobody could be successful in today’s competitive landscape without at least a moderate degree of leverage. Or more broadly, most corporations have sizable debt. If operating debt-free was such a superior business practice we should have already seen the emergence of “Big-Debt-Free, Inc.” driving all the existing leveraged corporations out of business and taking over the world. Competitive forces work swiftly in the business world! The fact that we haven’t seen the competitive pressure to eradicate debt implies that moderate leverage can’t be all that bad. Just like one beer a day supports your heart health!

All of our investments use leverage. We invested in real estate through several Private Equity funds that buy and/or develop multi-family housing. They all use leverage to juice up returns. In fact, without leverage, the projected net returns wouldn’t attract any investors. Or another example: our 3x leverage put writing strategy we have been running for a number years already. There isn’t really explicit debt involved because futures and futures options all trade on margin, but economically it’s equivalent to getting a loan at the rate of overnight cash and levering up this baby 3x! So wherever you look in finance there’s leverage and it’s not all bad.

We face this dilemma all the time. An investment opportunity emerges or we get a capital call from a private equity fund to transfer a pretty substantial sum within one week. Where do we get the money? The next bonus payment is a few months way. We could sell some investments, but then we’d incur capital gains. Even if they are long-term gains we’d prefer to defer them until they are taxed at a lower rate (or zero) in retirement. So, we simply borrow the money, short-term, until the next bonus season. The HELOC charges about 4% p.a. and Interactive Brokers charges about 2% p.a. in our margin account. For a few weeks or months, the interest cost is a rounding error compared to the fat tax bill.

Huh? How is that possible? Leverage makes all investments riskier all the time, right? That depends on the nature of the risk. Aggregate vs. Idiosyncratic. Would I rather invest in three real estate properties all paid in cash or 10 properties each with a 70% mortgage? If I can spread around the idiosyncratic risk of vacancies, major repairs, mold problems, hurricanes, earthquakes, lawsuits, etc. over a larger number of properties and over a wider geographic area, I’m all for it! Additionally, talking about lawsuits, as we pointed out before, a mortgage on a property could serve as a poison pill against greedy lawyers trying to sue you and a put option on the property value in case of idiosyncratic catastrophic losses. If used in moderation debt can *reduce* risk, too.

Another favorite pastime in the finance community: Paying off the mortgage way ahead of time. Here’s one reason why that’s a bad idea: **Sequence of Return Risk. **What does a mortgage have to do with sequence of return risk, something normally associated with the withdrawal phase in retirement? Low returns early on and high returns later will be worse for your retirement sustainability than high returns early on and low returns later. The opposite is true during the accumulation phase. All else equal, you’d strongly prefer low returns early on and high returns later while steadily saving every month. The timing of high versus low return adds risk to your IRR during the accumulation phase.

So, let’s look at two friends Adam and Betsy. Both have a $200,000, 30-year mortgage at 4% interest.

- Adam scrapes together every last penny every month and pays $2,094.90 per month instead of the required mortgage payment of $954.83. Doing so he can pay off the mortgage in 10 years and save a ton of money on interest. He can also start saving the entire $2,094.90 every month starting in year 11. Suze Orman would be proud of him!
- Betsy pays only the required $954.83 every month and saves $1,070.07 in an equity index fund.

After 30 years, of course, Betsy comes out ahead significantly, by more than 20%, even assuming a modest 7% (nominal) equity return (even assuming zero advantage from the mortgage interest deductibility). We knew that. But: because Betsy spread out her investments *more evenly* over the 30 years she is less subject to the dreaded sequence of return risk. Higher return and lower risk. All thanks to *not* paying down the mortgage faster than necessary!

OK, we can already foresee the angry comments, but please hear us out. The idea goes as follows: Would you rather have an emergency fund invested in cash (current yield maybe 1%) and forego an expected equity expected return of, let’s say, 7% or keep your investments in productive assets and use debt to finance the occasional emergency? The emergency fund is a constant drag of 6% p.a. (=expected equity over cash return). **If** emergencies come about with a **low enough probability** (say 10%) then even paying a substantial interest rate on the emergency debt should beat the permanent emergency fund.

Even a credit card balance at 18-20% annual interest, if used only 10% of the time, easily beats the permanent emergency fund: 0.1 x 20%=2% < 6% =1.0 x 6%. But debt doesn’t even have to be that expensive: We’re talking about 4% interest on a home equity line of credit (HELOC), which we use as our emergency fund. Even if you don’t own a home, banks offer reasonably priced lines of credit as pointed out in this excellent post the other day to be used in cases of short-term cash flow needs. Of course, all of this requires responsible use of debt. If you face one emergency after the other and you constantly have to tap your emergency fund then please don’t go into debt. But, as we have written before, a lot of home and car repairs and maintenance expenses are not really emergencies, they should be budget items. If we may quote ourselves **“Something breaking down is not an emergency. Something breaking down earlier than expected is an emergency.”**

For folks who are concerned about the loss of purchasing power, there is almost no better way to hedge against inflation than having nominal debt, ideally with a fixed interest rate. We currently have a mortgage with a $500k+ balance and the thought of 2% inflation p.a. chipping away at our mortgage balance to the tune of over $10,000 a year gives us a warm and fuzzy feeling. And that’s before Papa ERN pours the Single Malt Scotch (in moderation, naturally).

OK, we can already hear the objections: Of course, the $500K+ in additional investments we now own because we didn’t pay down the mortgage also melt away due to 2% inflation. True, but our investments are in equities and real estate. Corporate profits, rental income, and real estate values will eventually catch up with inflation. The decline in the purchasing power of the mortgage balance that our lender suffers, on the other hand, *is* *permanent*.

Sometimes cash is king, of course. If you bid in a foreclosure auction you better have a cashier’s check with you. Most of the time, sellers prefer buyers with a cash offer: it removes one additional uncertainty because buyers with a mortgage could still lose their funding in the last minute and cause the deal to fall through. Jon Dulin at MoneySmartGuides saved a ton of money when he used his cash on hand as a bargaining chip in negotiating a lower price with a seller. Of course, that still doesn’t mean you should avoid debt at all costs and all the time. One could pay cash to *close* the transaction quickly with the seller but then *get a mortgage afterward*. And then use the proceeds of the mortgage for the next transaction. Juice up returns (see #1) and spread the idiosyncratic risk over more properties (see #3)!

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